We begin with some general state space Markov chain theory. Let \(E\) 
be a set, and let \({\cal E}\)  be a countably generated \(\sigma \) -algebra
of subsets of \(E\) . Let \(P: E \times {\cal E} \rightarrow [0,1]\)  be a
Mtk, and assume that the corresponding Markov chain is irreducible,
aperiodic and positive Harris recurrent. (See [1]}
for definitions.) Let \(\Pi \)  denote the unique invariant probability
measure, and let \(P^n\)  denote the \(n\) -step Mtk (so, as usual, \(P\equiv P^1\) ). If \(\mu \)  is a probability measure on \(E\) , then we use
\(\mu P^n(\cdot )\)  to denote the probability measure \(\int _EP^n(u,\cdot ) \mu (du)\) . Following [2]} and
[3]}, we say that the Markov chain is
geometrically ergodic if there exist a non-negative extended
real-valued function \(M\)  with \(\int _E M(u) \, \Pi (du) < \infty \)  and a
\(\rho \in [0,1)\)  such that
\(\Vert P^n(u,\cdot ) - \Pi (\cdot )\Vert  \le M(u) \rho ^n\) 
